237 lines
9.1 KiB
Matlab
237 lines
9.1 KiB
Matlab
clear
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clc
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% yalmip('clear')
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addpath('.\Powerflow')
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[~, ~, ~, ~,Volt,Vangle,Y,Yangle,r,c,newwordParameter,PG,QG,PD,QD,Balance]=pf('ieee4.dat', '0');
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%% 量测量
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% 电压 节点电流 支路电流 节点功率 支路功率
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%%
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%% 状态量
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% 电压 相角
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%%
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%% 开始生成量测量
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sigma=0.05;% 标准差
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%% 电压
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%电压幅值
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rVolt=Volt; %幅值
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BalanceVolt=Volt(Balance);
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mVolt=rVolt.*(normrnd(0,sigma,length(Volt),1)+1);%电压量测量
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rVAngel=Vangle;
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%% 电流
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%注入电流
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cmpY=Y.*exp(1j*sparse(r,c,Yangle,length(Y),length(Y)));%复数导纳矩阵
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cmpV=Volt.*exp(1j*Vangle); %复数电压
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cmpI=cmpY*cmpV;% 注入电流
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rI=abs(cmpI); %注入电流量测量要的是电流幅值
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mI=rI.*(normrnd(0,sigma,length(rI),1)+1);%电流量测量
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%% 支路电流
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% 支路电流
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lineI=newwordParameter.line.lineI;
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lineJ=newwordParameter.line.lineJ;
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lineR=newwordParameter.line.lineR;
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lineX=newwordParameter.line.lineX;
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lineB2=newwordParameter.line.lineB2;
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lineG=real(1./(lineR+1j*lineX));
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lineB=imag(1./(lineR+1j*lineX));
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cmpBranchI=BranchI( cmpV,lineI,lineJ,lineR,lineX );%复数支路电流
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rBranchI=abs(cmpBranchI);% 支路电流幅值
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mBranchI=rBranchI.*(normrnd(0,sigma,length(rBranchI),1)+1);%支路电流量测量
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%% 支路功率
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rBranchP= BranchP( cmpV,cmpBranchI,lineI,lineB2 );
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mBranchP=rBranchP.*(normrnd(0,sigma,length(rBranchP),1)+1);%支路功率量测量
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rBranchQ=BranchQ( cmpV,cmpBranchI,lineI,lineB2 );
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mBranchQ=rBranchQ.*(normrnd(0,sigma,length(rBranchQ),1)+1);%支路功率量测量
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%% 注入功率
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rPD=PD;
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PDi=find(PD~=0);
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rQD=QD;
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QDi=find(QD~=0);
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rPG=PG;
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PGi=find(PG~=0);
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rQG=QG;
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QGi=find(QG~=0);
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mPD=rPD.*(normrnd(0,sigma,length(rPD),1)+1);
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mQD=rQD.*(normrnd(0,sigma,length(rQD),1)+1);
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mPG=rPG.*(normrnd(0,sigma,length(rPG),1)+1);
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mQG=rQG.*(normrnd(0,sigma,length(rQG),1)+1);
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%% 0注入节点
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zerosInjectionIndex=1:length(Volt);
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zerosInjectionIndex=zerosInjectionIndex( ~(PD~=0|QD~=0|PG~=0|QG~=0) );
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%% 变压器功率
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transI=newwordParameter.trans.transI;
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transJ=newwordParameter.trans.transJ;
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transK=newwordParameter.trans.transK;
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transR=newwordParameter.trans.transR;
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transX=newwordParameter.trans.transX;
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transG=real(1./(transR+1j*transX));
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transB=imag(1./(transR+1j*transX));
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rTransP=TransPower( newwordParameter,rVolt,rVAngel );
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rTransQ=TransReactivePower( newwordParameter,rVolt,rVAngel );
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mTransP=rTransP.*(normrnd(0,sigma,length(rTransP),1)+1);
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mTransQ=rTransQ.*(normrnd(0,sigma,length(rTransQ),1)+1);
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%% 发电机注入功率
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% 先找到只有发电机的节点
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PDQDi=union(PDi,QDi);
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onlyPG=setdiff(PGi,PDQDi);
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onlyQG=setdiff(QGi,PDQDi);
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%% 冗余度计算
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stateVarCount=2*length(Volt);
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measurements=length(mVolt)+length(mBranchI)+length(mBranchP)+length(mBranchQ)+length(mPG)+length(mQG)+length(mTransP)+length(mTransQ);
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fprintf('冗余度 %f\n',measurements/stateVarCount);
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%% Opti ToolBox
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Busnum=length(Volt);
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%% save
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% save('mVolt','mVolt');
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% save('mPG','mPG');
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% save('mQG','mQG');
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% save('mBranchI','mBranchI');
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% save('mBranchP','mBranchP');
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% save('mBranchQ','mBranchQ');
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% save('mTransP','mTransP');
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% save('mTransQ','mTransQ');
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%% load
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% load('mVolt');
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% load('mPG');
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% load('mQG');
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% load('mBranchI');
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% load('mBranchP');
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% load('mBranchQ');
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% load('mTransP');
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% load('mTransQ');
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%% 自己写的微分代码
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% 以下都是Jacobi矩阵
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SEVolt=sparse(ones(length(mVolt),1));
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SEVAngel=sparse(zeros(length(mVolt),1));
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maxD=1000;
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Iteration=0;
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while maxD>1e-3;
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% 电压
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dV_dV=sparse(1:length(mVolt),1:length(mVolt),1,length(mVolt),length(mVolt));%电压量测量的微分
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dV_dTyta=sparse(length(mVolt),length(mVolt));
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% 线路支路
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dLPij_dVi=sparse(1:length(lineI),lineI, ...
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-SEVolt(lineJ).*( ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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)...
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+2*(lineG).*SEVolt(lineI) ...
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,length(lineI),length(mVolt));%线路的
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dLPij_dVj=sparse(1:length(lineI),lineJ, ...
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-SEVolt(lineI).*( ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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) ...
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,length(lineI),length(mVolt));%线路的
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dLPij_dThetai=sparse(1:length(lineI),lineI, ...
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SEVolt(lineI).*SEVolt(lineJ).*( ...
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lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
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)...
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,length(lineI),length(mVolt));%线路的
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dLPij_dThetaj=sparse(1:length(lineI),lineJ, ...
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-SEVolt(lineI).*SEVolt(lineJ).*( ...
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lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
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)...
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,length(lineI),length(mVolt));%线路的
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dLQij_dVi=sparse(1:length(lineI),lineI, ...
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-SEVolt(lineJ).*( ...
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lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
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)...
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-2*(lineB+lineB2).*SEVolt(lineI) ...
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,length(lineI),length(mVolt));%线路的
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dLQij_dVj=sparse(1:length(lineI),lineJ, ...
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-SEVolt(lineI).*( ...
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lineG.*sin(SEVAngel(lineI)-SEVAngel(lineJ)) -lineB.*cos(SEVAngel(lineI)-SEVAngel(lineJ))...
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) ...
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,length(lineI),length(mVolt));%线路的
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dLQij_dThetai=sparse(1:length(lineI),lineI, ...
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-SEVolt(lineI).*SEVolt(lineJ).*( ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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) ...
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,length(lineI),length(mVolt));%线路的
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dLQij_dThetaj=sparse(1:length(lineI),lineJ, ...
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SEVolt(lineI).*SEVolt(lineJ).*( ...
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lineG.*cos(SEVAngel(lineI)-SEVAngel(lineJ)) +lineB.*sin(SEVAngel(lineI)-SEVAngel(lineJ))...
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) ...
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,length(lineI),length(mVolt));%线路的
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% 变压器支路
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dTPij_dVi=sparse(1:length(transI),transI, ...
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-SEVolt(transJ)./transK.*( ...
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transG.*cos(SEVAngel(transI)-SEVAngel(transJ)) +transB.*sin(SEVAngel(transI)-SEVAngel(transJ))...
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)...
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+2*transG.*SEVolt(transI)./(transK.^2) ...
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,length(transI),length(mVolt));%变压器
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dTPij_dVj=sparse(1:length(transI),transJ, ...
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-SEVolt(transI)./transK.*( ...
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transG.*cos(SEVAngel(transI)-SEVAngel(transJ)) +transB.*sin(SEVAngel(transI)-SEVAngel(transJ))...
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) ...
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,length(transI),length(mVolt));%变压器
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dTPij_dThetai=sparse(1:length(transI),transI, ...
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SEVolt(transI)./transK.*SEVolt(transJ).*( ...
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transG.*sin(SEVAngel(transI)-SEVAngel(transJ)) -transB.*cos(SEVAngel(transI)-SEVAngel(transJ))...
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)...
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,length(transI),length(mVolt));%变压器
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dTPij_dThetaj=sparse(1:length(transI),transJ, ...
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-SEVolt(transI)./transK.*SEVolt(transJ).*( ...
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transG.*sin(SEVAngel(transI)-SEVAngel(transJ)) -transB.*cos(SEVAngel(transI)-SEVAngel(transJ))...
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)...
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,length(transI),length(mVolt));%变压器
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dTQij_dVi=sparse(1:length(transI),transI, ...
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-SEVolt(transJ)./transK.*( ...
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transG.*sin(SEVAngel(transI)-SEVAngel(transJ)) -transB.*cos(SEVAngel(transI)-SEVAngel(transJ))...
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)...
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-2*transB.*SEVolt(transI)./(transK.^2) ...
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,length(transI),length(mVolt));%变压器
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dTQij_dVj=sparse(1:length(transI),transJ, ...
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-SEVolt(transI)./transK.*( ...
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transG.*sin(SEVAngel(transI)-SEVAngel(transJ)) -transB.*cos(SEVAngel(transI)-SEVAngel(transJ))...
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) ...
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,length(transI),length(mVolt));%变压器
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dTQij_dThetai=sparse(1:length(transI),transI, ...
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-SEVolt(transI)./transK.*SEVolt(transJ).*( ...
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transG.*cos(SEVAngel(transI)-SEVAngel(transJ)) +transB.*sin(SEVAngel(transI)-SEVAngel(transJ))...
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) ...
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,length(transI),length(mVolt));%变压器
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dTQij_dThetaj=sparse(1:length(transI),transJ, ...
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SEVolt(transI)./transK.*SEVolt(transJ).*( ...
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transG.*cos(SEVAngel(transI)-SEVAngel(transJ)) +transB.*sin(SEVAngel(transI)-SEVAngel(transJ))...
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) ...
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,length(transI),length(mVolt));%变压器
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%% 进入迭代
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% H=[dV_dV ,dV_dTyta;
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% dLPij_dVi+dLPij_dVj, dLPij_dThetai+dLPij_dThetaj;
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% dLQij_dVi+dLQij_dVj, dLQij_dThetai+dLQij_dThetaj];%jacobi
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H=[dV_dV,dV_dTyta;
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dLPij_dVi+dLPij_dVj,dLPij_dThetai+dLPij_dThetaj ;
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dLQij_dVi+dLQij_dVj,dLQij_dThetai+dLQij_dThetaj ;
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dTPij_dVi+dTPij_dVj,dTPij_dThetai+dTPij_dThetaj;
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dTQij_dVi+dTQij_dVj,dTQij_dThetai+dTQij_dThetaj];%jacobi
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SEBranchI=BranchI( SEVolt.*exp(1j*SEVAngel),lineI,lineJ,lineR,lineX );%复数支路电流
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SEBranchP=BranchP( SEVolt.*exp(1j*SEVAngel),SEBranchI,lineI,lineB2 );
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SEBranchQ=BranchQ( SEVolt.*exp(1j*SEVAngel),SEBranchI,lineI,lineB2 );
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SETransP=TransPower( newwordParameter,SEVolt,SEVAngel );
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SETransQ=TransReactivePower( newwordParameter,SEVolt,SEVAngel );
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h=[SEVolt;SEBranchP;SEBranchQ;SETransP;SETransQ];
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z=[mVolt;mBranchP;mBranchQ;mTransP;mTransQ];
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W=sparse(1:length(h),1:length(h),1/sigma.^2,length(h),length(h));
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G=H'*W*H;
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g=-H'*W*(z-h);
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% 平衡节点相角恒定;
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G(length(mVolt)+Balance,:)=0;
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G(:,length(mVolt)+Balance)=0;
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G=G+sparse(length(mVolt)+Balance,length(mVolt)+Balance,1,length(mVolt)*2,length(mVolt)*2);
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g(length(mVolt)+Balance)=0;
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dX=G\-g;
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maxD=max(abs(dX))
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% 更新变量
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SEVolt=SEVolt+dX(1:length(mVolt));
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Iteration=Iteration+1;
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SEVAngel=SEVAngel+dX(length(mVolt)+1:end);
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end
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%% 输出结果
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fprintf('迭代%d次\n',Iteration);
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fval=full((z-h)'*W*(z-h));
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fprintf('目标函数为:%f\n',fval);
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fprintf('相对误差\n');
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(abs(rVolt-double(SEVolt)))./(rVolt)
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MaxDeviation(rVolt,SEVolt,rVAngel,SEVAngel)
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plotAndComparison( rVolt,rVAngel,SEVolt,SEVAngel ) |